Question

Find x and explain how you found it!

Answer 1

Here we use trigonometric ratios

`\\ \rm\hookrightarrow sin\theta=(Perpendicular)/(Hypotenuse)`

`\\ \rm\hookrightarrow sin53=(x)/(24)`

`\\ \rm\hookrightarrow 0.8(24)=x`

`\\ \rm\hookrightarrow x=19.2`

Answer 2

`\Large\boxed{\sf x = 19.2}`

Explanation:

Here a right angled triangle is given to us and we need to find out the value of x . The measure of one of the sides is 24 and one of the acute angle is 53° .

• Here 24 is hypotenuse of the triangle and x is the perpendicular .

So here we may use the ratio of sine as ,

`\sf\qquad\longrightarrow sin\theta =(p)/(h) \\\\`

• On substituting the respective values ,

`\sf\qquad\longrightarrow sin53^\circ =(x)/(24)\\\\`

Substitute the value of sin 53° = 4/5 ,

`\sf\qquad\longrightarrow (4)/(5)=(x)/(24) \\\\`

Cross multiply ,

`\sf\qquad\longrightarrow x =(24*4)/(5) \\\\`

Simplify,

`\sf\qquad\longrightarrow \frak{\pink{x =19.2}} \\\\`

`\rule{200}4`